\brief \b ESMF_DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. \htmlonly Download ESMF_DLAED2 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:
\verbatim
ESMF_DLAED2 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. \endverbatim \param[out] K \verbatim K is INTEGER The number of non-deflated eigenvalues, and the order of the related secular equation. 0 <= K <=N. \endverbatim
\param[in] N \verbatim N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. \endverbatim
\param[in] N1 \verbatim N1 is INTEGER The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= N1 <= N/2. \endverbatim
\param[in,out] D \verbatim D is DOUBLE PRECISION array, dimension (N) On entry, D contains the eigenvalues of the two submatrices to be combined. On exit, D contains the trailing (N-K) updated eigenvalues (those which were deflated) sorted into increasing order. \endverbatim
\param[in,out] Q \verbatim Q is DOUBLE PRECISION array, dimension (LDQ, N) On entry, Q contains the eigenvectors of two submatrices in the two square blocks with corners at (1,1), (N1,N1) and (N1+1, N1+1), (N,N). On exit, Q contains the trailing (N-K) updated eigenvectors (those which were deflated) in its last N-K columns. \endverbatim
\param[in] LDQ \verbatim LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N). \endverbatim
\param[in,out] INDXQ \verbatim INDXQ is INTEGER array, dimension (N) The permutation which separately sorts the two sub-problems in D into ascending order. Note that elements in the second half of this permutation must first have N1 added to their values. Destroyed on exit. \endverbatim
\param[in,out] RHO \verbatim RHO is DOUBLE PRECISION On entry, the off-diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined. On exit, RHO has been modified to the value required by ESMF_DLAED3. \endverbatim
\param[in] Z \verbatim Z is DOUBLE PRECISION array, dimension (N) On entry, Z contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix). On exit, the contents of Z have been destroyed by the updating process. \endverbatim
\param[out] DLAMDA \verbatim DLAMDA is DOUBLE PRECISION array, dimension (N) A copy of the first K eigenvalues which will be used by ESMF_DLAED3 to form the secular equation. \endverbatim
\param[out] W \verbatim W is DOUBLE PRECISION array, dimension (N) The first k values of the final deflation-altered z-vector which will be passed to ESMF_DLAED3. \endverbatim
\param[out] Q2 \verbatim Q2 is DOUBLE PRECISION array, dimension (N12+(N-N1)2) A copy of the first K eigenvectors which will be used by ESMF_DLAED3 in a matrix multiply (ESMF_DGEMM) to solve for the new eigenvectors. \endverbatim
\param[out] INDX \verbatim INDX is INTEGER array, dimension (N) The permutation used to sort the contents of DLAMDA into ascending order. \endverbatim
\param[out] INDXC \verbatim INDXC is INTEGER array, dimension (N) The permutation used to arrange the columns of the deflated Q matrix into three groups: the first group contains non-zero elements only at and above N1, the second contains non-zero elements only below N1, and the third is dense. \endverbatim
\param[out] INDXP \verbatim INDXP is INTEGER array, dimension (N) The permutation used to place deflated values of D at the end of the array. INDXP(1:K) points to the nondeflated D-values and INDXP(K+1:N) points to the deflated eigenvalues. \endverbatim
\param[out] COLTYP \verbatim COLTYP is INTEGER array, dimension (N) During execution, a label which will indicate which of the following types a column in the Q2 matrix is: 1 : non-zero in the upper half only; 2 : dense; 3 : non-zero in the lower half only; 4 : deflated. On exit, COLTYP(i) is the number of columns of type i, for i=1 to 4 only. \endverbatim
\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date December 2016 \ingroup auxOTHERcomputational \par Contributors:
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA \n Modified by Francoise Tisseur, University of Tennessee
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer | :: | K | ||||
| integer | :: | N | ||||
| integer | :: | N1 | ||||
| double precision | :: | D(*) | ||||
| double precision | :: | Q(LDQ,*) | ||||
| integer | :: | LDQ | ||||
| integer | :: | INDXQ(*) | ||||
| double precision | :: | RHO | ||||
| double precision | :: | Z(*) | ||||
| double precision | :: | DLAMDA(*) | ||||
| double precision | :: | W(*) | ||||
| double precision | :: | Q2(*) | ||||
| integer | :: | INDX(*) | ||||
| integer | :: | INDXC(*) | ||||
| integer | :: | INDXP(*) | ||||
| integer | :: | COLTYP(*) | ||||
| integer | :: | INFO |